This paper proposes an analysis of the manipulability of the Center of Mass (CoM) of humanoid robots. Starting from the dynamic equations of humanoid robots, the operational space formulation is used to express the dynamics of humanoid robots at their CoM and under their specific characteristics: a free-floating base, forces at contact points, and dynamic balance constraints. After a review of the kinematic manipulability of the CoM, the concept of dynamic manipulability of the CoM is introduced. The latter represents the ability of a humanoid robot to generate a spatial motion under a stability criterion. The size and shape of the dynamic manipulability of the CoM are a function of the joint torque limitations, the contact forces and the zero moment point used as a stability criteria. Two calculations of the CoM dynamic manipulability are proposed, a fast ellipsoid approximation, and the exact polyhedron computation. A case study illustrates the proposed approach on the HOAP3 humanoid robot and its use for mechanical design optimization.
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